Mathematics - 2021-04-26 (page 3 of 3)

leslie townes

21:00

the US continued decision to tax worldwide income of nonresidents is confusing and probably causes more problems than it purports to solve. we're the only big nation that still does this.

for more, please subscribe to my fervently anti-tax newsletter at LeslieTownesTruth.com.

copper.hat

used to be i would call my friend in the bank and it was done. a few years ago they made me get a cheque countersigned by my almost 90yo mother in order to deposit it in my own account. we're talking something like $100 in accounts that have 50+ years standing and an obvious familial relationship.

there was that time i left a $20 in my jeans by mistake, maybe that was what triggered the laundering investigation...

leslie townes

you should just have them put the $100 into the next bag that goes from the pub in south boston to a pub in northern ireland. no tax on that.

for the record, please do not actually do that

copper.hat

my legal representation said to...

leslie townes

i was doing a parody.

one time we had a client who was sued by a tax cheat. he was being criminally prosecuted by the government at the same time he was suing us, it was kind of a race to see what would end first. his positions in the lawsuit were stupid but we admired the aggression of his tax positions.

he ended up losing both the lawsuit and his criminal case and is in jail now, but i still like some of his tax positions.

copper.hat

we used to have enough family members traveling that we could handle most small scale forex within the family (without that sounding a bit eyebrow raising). the argument was what rate to agree on.

leslie townes

21:10

i once smuggled a case full of wine into denmark. i secreted it in various portions of luggage and did not declare it. i think we saved something like 10 dollars.

copper.hat

we had some warrants at some stage and instead of exercising i asked the vcs if they would buy the warrants themselves instead, thus converting an income into a capital gain. they went along with it mainly because i think they thought it was cute.

leslie townes

well done.

copper.hat

i brought two new kayaks (along with 2 small children, not inside) into ireland once. customs did not even raise an eyebrow.

for personal use.

and then there was the diamond...

leslie townes

i also smuggled 20 kilos of cocaine into denmark. i hid it under wine bottles.

copper.hat

i was a little on edge until the statute of limitations expired on that one...

i hope you are kidding

leslie townes

21:13

yes, quite kidding. the wine was not a joke but if the danish government wants to fine me with interest that is OK.

copper.hat

there really was a diamond. i have no idea how much it cost. it was for a friend.

leslie townes

it would probably be 30 dollars now. i can afford that.

copper.hat

with whom i subsequently sailed acorss the irish sea.

leslie townes

diamonds are such a scam.

copper.hat

it could have been glass for all i know.

i agree entirely.

brilliant debeers marketing, created out of nothing.

leslie townes

21:15

you do get very cool patterns if you train a laser pointer on a well cut diamond in a darkened room. it does not justify the whole de beers thing, but if you've got one, try it and thank me later.

robjohn

My wife and I collect all sorts of less precious stones. I have some humongous emeralds, but they are not the nice clear kind that are very expensive.

copper.hat

we are modern women, look at my dowry

i like intriguing stuff like translucent rocks (albeit maybe only i find such things intriguing from a non commercial standpoint).

leslie townes

i wear a wedding ring that is made out of some kind of chromium alloy. i've spent more on sushi than i spent on the ring. i exemplify the virtue of thrift.

copper.hat

that's a story that has no current resolution in my family.

robjohn

@leslietownes I once wrote a program for my friend's Apple II that would allow him to draw something on his tablet and it would convert that into instructions to control galvanometers that moved small mirrors really fast to draw the same thing with lasers.

copper.hat

21:18

while i may say i am, i am not really a cheap bastard, but i will not willingly go further into debt to fund a debeer marketing campaign

robjohn

on the wall

leslie townes

whoops, typo there. i'm sorry you etched LESLIE TOWNES IS KING into your wall.

copper.hat

impressive actuators

i loved the IIe

leslie townes

i liked the IIgs.

copper.hat

i fell out with apple after that

esp when cook would not let us use the apple logo

but mainly when jobs stiffed woz

even though woz has forgiven him (i attended an interview with him)

leslie townes

21:20

our school had a number of IIes and a number of TRS-80s. my best friend in middle school had a IIgs, it was like being on another planet. graphics AND sound.

copper.hat

oohhh, the trs-80

leslie townes

they still had them in 1997 when i graduated. i remember being told to go do something and opening a utility closet, and it was full of trs-80s.

i should have stolen one.

copper.hat

i took one of my dad's colleagues one apart just to have a look, he left it in our house when he went on holidays

after opening it up, headlights appeared at the curtain, peter & family were back

omg

what a scramble. plus one screw left over.

leslie townes

one of my friends had a ZX spectrum, they were not very common in the united states. his dad was always in the UK on business.

copper.hat

that was scarier than walking around the edge of a water tower

i loved sinclair stuff

it was totally cool

leslie townes

21:22

it was really cool.

copper.hat

i had a little basic calculator by him

red led display in purple plastic, really awesome

but i still used my slide rule

leslie townes

he's still alive. and younger than i would have expected.

copper.hat

he was a real entrepreneur

leslie townes

tiny island full of people who are too clever for their own good.

copper.hat

very innovative people, rather unimaginative government

and then brexit (sounds of machine going haywire on this end)

leslie townes

21:25

the tradition of the amateur eccentric is something that the UK has somehow maintained better than most nations.

and yes all of that nonsense on the political level. i'm not one to talk, i live in the USA.

Flows.

brexit is so sad

what was the point of the last 100 years

leslie townes

if i punch myself hard enough in the face, you'll all be sorry that i did it

Flows.

(and more)

copper.hat

is suspect there was a correlation, so of the best from each side colluded, nigel, bannon

i agree that there was much eu overstepping

Flows.

guys

copper.hat

21:27

but deal with that, not throw everything out

Flows.

I thought you did math so you didnt have to think about politics

leslie townes

i think about politics so i don't have to do math.

copper.hat

how else can i keep my blood pressure up?

Flows.

fair

how is Villani's political career going?

I havent followed at all

leslie townes

is he still doing that?

Flows.

21:28

I assume so

copper.hat

ghouliani?

leslie townes

i remember when he was just a guy on a postdoc.

i promise everybody that whatever happens i will not transition into politics.

copper.hat

what about mathematics?

i think they should standardise some aspects of law to make worldwide operation easier.

leslie would be perfect for that

BigSocks

22:05

I get that this may be unappealing to many, but is there a way to take a (finite) quasigroup (that is not a group, but is otherwise as nice as you like) and build a (finite or at worst countable) group that contains the original quasigroup (at least the elements and products).

I've tried a few things, but it seems that there's no reasonable way to "repair" the quasigroup. I was thinking of 2-groups and how they are basically crossed modules of groups, so you have elements and functions and they intermingle, but it is an operation that is kind of "closed" under groups. Similarly you could t…

user863565

23:08

Gabriel horn hold finite amount of paint but there is not enough paint in the world to paint it

copper.hat

it comes from a non measurable paint can.

Ted Shifrin

I love Gabriel's horn.

Great to watch students struggle with this.

copper.hat

There must be easier ways of demonstrating that, fanfolds of ever increasing angle?

Ted Shifrin

Is that a non-measurable can or non-measurable paint?

Who of what?

copper.hat

infinite area, finite volume...

i am hearing voices...

BigSocks

23:17

isn't it just a couple of integrals?

Ted Shifrin

Leslie has corrupted you.

copper.hat

my corruption predated Leslie, albeit he has not improved the situation

Ted Shifrin

That doesn’t explain the paradox, Big.

BigSocks

integral for volume is finite, the one for surface area is infinite

Ted Shifrin

No, he's worsened you.

Duh. So?

BigSocks

23:19

that's what I'm saying

Ted Shifrin

The question is a common sense question. You're not addressing it.

BigSocks

I don't understand. what's the question? "How is that possible?" or something like that

Ted Shifrin

Yes

Not a question of abstract math.

BigSocks

then of what? philosophy? linguistics?

and how then could we address it other than how we have ?

Ted Shifrin

Why do I not paint the “sides” of the can when I fill it up?

copper.hat

23:22

to some degree we think of area as 'incremental volume', so when one is infinite and one is finite it 'contradicts' our thought process and is curious

BigSocks

@TedShifrin Hmm... I guess I never thought much more of this. I guess I could just say "paint is not well defined", but that seems unsatisfying

Ted Shifrin

That's crap.

copper.hat

well, many things that need careful definition have a working intuition that applies in many 'nice' situations.

and that is the starting point for many fruitful journeys

Thorgott

misguiding question, you do paint the sides

Ted Shifrin

Not in any physical sense you don't.

BigSocks

23:28

Eh, I think it is kind of crap to assume such an object could exist in the same way paint could exist

Ted Shifrin

You can make it into a finite question.

With one number very finite and the other as yuge as we want.

Thorgott

then I'll have to switch to the "painting doesn't make sense" side

if filling the interior of a shape up with paint doesn't paint the surface, I don't know what painting is

BigSocks

exactly

copper.hat

well, it is about how much paint you need.

Ted Shifrin

Well, that's a good question. As I said, it's physical, not philosophical.

copper.hat

23:31

just as brownian motion

BigSocks

@copper.hat ?

Thorgott

yeah, the amount is the issue, but that's not my point

Ted Shifrin

If you have the answer, don’t spoil it for others.

BigSocks

@TedShifrin makes it sound like limits, picking $\epsilon$s and $\delta$s

Ted Shifrin

My standard leading question to students is this: if you want to paint the walls of a room, why do you go buy gallons (cu ft or cu m) of paint?

BigSocks

23:33

@TedShifrin but still, very weird to think of a "physical object of infinite spacial extent"

paint (and most real things) have thickness?

Ted Shifrin

Can you make that thickness arbitrarily small?

BigSocks

not in real life I don't think, but I think the correct answer might be "yes"

copper.hat

@BigSocks in a vaguely related sense, a Brownian motion path has unbounded variation but finite distance.

it does not mean that length is not well defined.

Ted Shifrin

Maybe it's better to ask if you can fill the paint can as you thought you could.

Thorgott

infinity doesn't exist in real life

Ted Shifrin

23:36

I keep saying you don't need infinity.

copper.hat

many chemical designs try to achieve maximal area in a given volume.

batteries, water, etc

@Thorgott are there points missing from $[0,1]$? :-)

Ted Shifrin

Good point! :D

Koro

How do I find nth term of this sequence:

copper.hat

it is:

Koro

1,2,2,3,3,3,4,4,4,4,...

Ted Shifrin

23:41

Count.

Koro

Observations: 1) nth term $T_n\le n$

Hi @ Tedshifrin: Counting is the problem. If I could find sum of first n terms then also I’ll be done

This question is solvable. It’s just that how can somebody (who has not invented this exercise) can solve it

?

BigSocks

why would inventing it give you a privileged position to solving it?

copper.hat

Solve $\max \{ m | S_m \le n \}$.

Ted Shifrin

Figure out where the last number $k$ is.

Koro

There are also a few answers to this question on this website.

leslie townes

23:46

i get something with a ceiling and square roots.

Koro

@TedShifrin ok thanks a lot. I’ll try that.

@copper.hat Ok I’ll try that as well.

Thanks a lot @copper.hat

:57784842: Indeed the final answer involves those. :)

copper.hat

what is 57784842?

leslie townes

of course i'm off by one. i had to fix that.

Koro

I clicked on reply to @leslietownes and that number came @copper.hat

copper.hat

very suspicious. his hourly billing rate i imagine

leslie townes

23:50

copper, we're all robots. that's my serial number. beep boop.

Koro

Haha :D

leslie townes

when i lived in iowa my phone number was a prime number. i wish i still had it.

copper.hat

i get $\lceil { \sqrt{1+4n^2}-1 \over 2} \rceil$, but have been known not to make a mistake from time to time.

poor divisible numbers.

leslie townes

i had ceiling of (1/2)sqrt(8n+1) - 1.

maybe if we average the two.

copper.hat

mine is wrong, of course, apparently $2 \cdot 4$ is $8$ now.

how embarrasing.

Ted Shifrin

23:55

Huh?

leslie townes

they introduced that with the 2021 line of 8s.

copper.hat

i goofed in my computation

i thought with inflation an all..

Ted Shifrin

You mean $2\cdot 4$ isn’t $8$?

copper.hat

in joe's world

Ted Shifrin

Cool

copper.hat

23:57

when traveling at the speed of slight

by a process of iterative refinement i now pronounce Leslie's answer correct.

if only i had not solved this particular problem, oohh, a hundred times before.

leslie townes

we have to deduct a 10% "tax" paid to a guy in platform shoes and bell bottoms.

copper.hat

i believe the bell bottoms are in the skip now.

never had platforms, but did have quarter irons.

to pretend to be a tough guy. how risable.

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$Mathematics$ Mathematics